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arXiv:1307.7175 · Physical Review Letters

Three-Dimensional Anderson Localization in Variable Scale Disorder

William McGehee, Stanimir Kondov, Wenchao Xu, J. J. Zirbel, Brian DeMarco

Published Oct 2, 2013• 46 citations
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Abstract

We report on the impact of variable-scale disorder on 3D Anderson localization of a noninteracting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of 4 via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.

DOI
10.1103/physrevlett.111.145303

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Comment on “Three-Dimensional Anderson Localization in Variable Scale Disorder”

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In a recent experiment [McGehee et al., Phys. Rev. Lett. 111, 145303 (2013)], the expansion of non-interacting ultracold fermions was studied in a random speckle potential, and the observed density profiles were interpreted based on 3D Anderson localization. The purpose of this note is to demonstrate that slow diffusion of particles with a broad energy distribution and an energy-dependent diffusion coefficient leads to density profiles that agree with the measured data, but not with the behavior expected for 3D Anderson localization.

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Three-dimensional Anderson localization

Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium.We observe three-dimensional AL of non-interacting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential.A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component.We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy.These measurements provide a benchmark for more sophisticated theories of AL.Wave propagation in disordered media is affected by scattering from random impurities.When those scattered waves self-interfere destructively, a phenomenon known as Anderson localization (AL) can arise (1).AL occurs in a wide variety of classical and quantum materials, impacting the transport of light (2, 3), acoustic (4), and matter (5, 6) waves.Localization is known to affect electrical conductivity in solids as a result of scattering from impurities and 1

Physics Today•Oct 31, 2011•0 citations
We report on the impact of variable-scale disorder on 3D Anderson localization of a noninteracting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of 4 via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.
We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.
In a recent experiment [McGehee et al., Phys. Rev. Lett. 111, 145303 (2013)], the expansion of non-interacting ultracold fermions was studied in a random speckle potential, and the observed density profiles were interpreted based on 3D Anderson localization. The purpose of this note is to demonstrate that slow diffusion of particles with a broad energy distribution and an energy-dependent diffusion coefficient leads to density profiles that agree with the measured data, but not with the behavior expected for 3D Anderson localization.
Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. We observe three-dimensional AL of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential. A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component. We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy. These measurements provide a benchmark for more sophisticated theories of AL.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold gases has been elusive. We show that a cause of this difficulty is the relatively high percolation threshold of a speckle potential in two dimensions, resulting in strong classical localization. We propose a realistic pointlike disorder potential that circumvents this percolation limit with localization lengths that are experimentally observable. The percolation threshold is evaluated for experimentally realistic parameters, and a regime of negligible classical trapping is identified. Localization lengths are determined via scaling theory, using both exact scattering cross sections and the Born approximation, and by direct simulation of the time-dependent Schr\"odinger equation. We show that the Born approximation can underestimate the localization length by four orders of magnitude at low energies, while exact cross sections and scaling theory provide an upper bound. Achievable experimental parameters for observing localization in this system are proposed.
Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium.We observe three-dimensional AL of non-interacting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential.A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component.We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy.These measurements provide a benchmark for more sophisticated theories of AL.Wave propagation in disordered media is affected by scattering from random impurities.When those scattered waves self-interfere destructively, a phenomenon known as Anderson localization (AL) can arise (1).AL occurs in a wide variety of classical and quantum materials, impacting the transport of light (2, 3), acoustic (4), and matter (5, 6) waves.Localization is known to affect electrical conductivity in solids as a result of scattering from impurities and 1